Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215 |
| direct product | C25×D23 |
| unambiguous semidirect product | C23⋊C26 |
| unambiguous semidirect product | (C2×C23)⋊C25 |
| Fitting, socle | C25×C23 ⋊ C2 |
| derived, Sylow | C23 ⋊ C26 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D23 |
| commutator, cosocle, hypocenter | C23 | C26 |
| Frattini | C1 | G |
| Fitting, socle | C25×C23 | C2 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C25 | |
5650 conjugacy classes of subgroups.
| transitive degree | μt(G) = 736 |
416 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×#379, C2×#13092272, #15681673, … |
| maximal normal subgroup of | D23×#379, C2×#13092272, #15681673, … |
| maximal quotient of | C24×C4×D23, C25×Dic23, C23×D4×D23, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 1387);